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DOI: 10.23952/jnfa.2025.17
Received February 3, 2025; Accepted May 23, 2025; Published June 22, 2025
Abstract. In this paper, we introduce a modification of the forward-backward splitting algorithm with different step-size rules for a monotone inclusion problem and a fixed point problem of a nonexpansive mapping. Our algorithm is based on the Mann viscosity and Tseng type methods. Under some assumptions, such as Lipschitz continuous and monotone, we obtain a strong convergence theorem of common solutions in Hilbert spaces. Finally, we also apply our theorem to some problems and provide numerical examples to support the effectiveness of our algorithm.
How to Cite this Article:
T. Jitpeera, M. Suwannaprapa, Mann viscosity Tseng type method for inclusion and fixed point problems in Hilbert spaces, J. Nonlinear Funct. Anal. 2025 (2025) 17.